from manim import *



class math1(MovingCameraScene):
    def construct(self):
        self.camera.background_color = BLACK  # 设置背景颜色
        self.camera.frame_width = 100  # 设置边框宽度
        self.camera.frame_height = 60  # 设置边框高度
        self.camera.pixel_height = 1080  # 设置像素高度
        self.camera.pixel_width = 1920  # 设置像素宽度
        self.camera.center = ORIGIN  # 设置中心点位置
        self.camera.scale_factor = 1.0  # 设置缩放因子
        #设置横线
        for i in range(6*2+1):       
            dot1=Dot([-50,5*(i-6),0]).set_opacity(0.5)
            dot2=Dot([50,5*(i-6),0]).set_opacity(0.5)
            if i==6:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
                
            else:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
               
            self.add(dot1,dot2,line1)
        #设置竖线
        for i in range(10*2+1):        
            dot3=Dot([(i-10)*5,-30,0]).set_opacity(0.5)
            dot4=Dot([(i-10)*5,30,0]).set_opacity(0.5)
            if i==10:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
                
            else:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
            self.add(dot3,dot4,line2)
        #设置三个点
        dot1 = Dot(radius=1, color=RED)  
        dot1.move_to([-47.5,27.5,0]) 
        dot2 = Dot(radius=1, color=YELLOW)  
        dot2.move_to([-42.5,27.5,0])  
        dot3 = Dot(radius=1, color=GREEN)  
        dot3.move_to([-37.5,27.5,0])
        #镜头跟进效果 
        self.camera.frame.save_state()
        #题目出现
        text = Tex(r"\text{设}$f\left( x\right) $\text{为连续函数，且}$\int _{0}^{\pi }f\left( x\sin x\right) \sin xdx=1\text{，则}$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0)
        text1 = Tex(
                   r"$\int _{0}^{\pi }f\left( x\sin x\right) x\cos xdx=$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-15,-5,0])

        self.play(Write(text),self.camera.frame.animate.scale(0.8))
        self.play(Write(text1))
        self.wait()
        #镜头拉回
          #分析文本
        text100=MarkupText("<b><i>分析/解：</i></b>",color=PINK).scale(5.0).move_to([-38,12.5,0])
        self.play(Restore(self.camera.frame))
        self.play(Create(text100),FadeIn(dot1),run_time=0.1)
        self.play(FadeIn(dot2),run_time=0.1)
        self.play(FadeIn(dot3),run_time=0.1)
        #题目向上移动
        self.play(text.animate().move_to([0,20,0]),text1.animate().move_to([-15,15,0])) 


         #半透明矩阵扩展
        rectangle=Rectangle(color=BLUE,fill_opacity=0.3,width=1,height=2.8
                            ,stroke_color=YELLOW,stroke_width=0).move_to([10,20,0])

        rectangle1=Rectangle(color=BLUE,fill_opacity=0.3,width=1,height=2.8
                            ,stroke_color=YELLOW,stroke_width=0).move_to([-15,15,0])
        self.play( 
            rectangle1.animate.stretch(25.0,dim=0)
            ,rectangle.animate.stretch(28.0,dim=0) 
        )


        text2 = Tex(r"$\left( x\sin x\right) ^{'}=\sin x+x\cos x$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,10,0])
        self.play(Write(text2))

        text3 = Tex(r"$\int _{0}^{\pi }f\left( x\sin x\right) \sin xdx+\int _{0}^{\pi }f\left( x\sin x\right) x\cos xdx$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,5,0])
        self.play(Write(text3))

        text4 = Tex(r"$ =\int _{0}^{\pi }f\left( x\sin x\right) \left( \sin x+x\cos x\right) dx$"
                    ,color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-5,0,0])
        self.play(Write(text4))
        text5= Tex(r"$ =\int _{0}^{\pi }f\left( x\sin x\right) d\left( x\sin x\right) $"
                    ,color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-10,-5,0])
        self.play(Write(text5))
        text6= Tex(r"\text{令}$t=x\sin x$"
                    ,color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text5,RIGHT,buff=1)
        self.play(Write(text6))

        text7= Tex(r"$=\int _{0}^{0}f\left( t\right) dt$"
                    ,color=PINK
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-17,-10,0])
        self.play(Write(text7))
        self.wait(0.3)
        text8= Tex(r"$=0$"
                    ,color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text7,RIGHT,buff=1)
        self.play(Write(text8))
        #框框标记
        
        rectangle2=Rectangle(color=BLUE,fill_opacity=0.0,width=23.5,height=5
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle2.move_to([-14, 5, 0])
        self.play(Create(rectangle2))
        #文本
        text9= Tex(r"$1$"
                    ,color=PURE_RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(10.0).move_to([-33,5,0])
        self.play(Write(text9))
        self.play(FadeOut(text9))
        self.wait(0.3)
        #框框移动
        self.play(rectangle2.animate().shift(27*RIGHT).set_width(25))
        text10= Tex(r"$?$"
                    ,color=PURE_RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(10.0).move_to([33,5,0])
        self.play(Write(text10))










        self.wait()